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Consider the setSnof all subsets of the set withnelements (nis a natural number here) For two such subsetsAandBdefine the distance betweenAandBas the number of elements

Consider the setSnof all subsets of the set withnelements (nis a natural number here) For two such subsetsAandBdefine the distance betweenAandBas the number of elements which belong to exaclty one of the sets (i.e. inAbut not inB, or inBbut not inA). Prove thatSnwith this distance is a metric space. Make sure sure you check all properties of metric.

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